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Gaussian-kernel c-means Clustering Algorithms

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Theory and Practice of Natural Computing (TPNC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11324))

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Abstract

K-means (or called hard c-means, HCM) and fuzzy c-means (FCM) are the most known clustering algorithms. However, the HCM and FCM algorithms work worse for the data set with different shape clusters in noisy environments. For solving these drawbacks in HCM and FCM, Wu and Yang (2002) proposed alternative c-means clustering that extends HCM and FCM into alternative HCM (AHCM) and alternative FCM (AFCM). In this paper, we further extend AHCM and AFCM as Gaussian-kernel c-means clustering, called GK-HCM and GK-FCM. Some numerical and real data sets are used to compare the proposed GK-HCM and GK-FCM with AHCM and AFCM methods. Experimental results and comparisons actually demonstrate these good aspects of the proposed GK-HCM and GK-FCM algorithms with its effectiveness and usefulness in practice.

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References

  1. Bandyopadhyay, S.: An automatic shape independent clustering technique. Pattern Recogn. 37, 33–45 (2004)

    Article  Google Scholar 

  2. Baraldi, A., Blonda, P.: A survey of fuzzy clustering algorithms for pattern recognition Part I and II. IEEE Trans. Syst. Man Cybern. Part B Cybern. 29, 778–801 (1999)

    Article  Google Scholar 

  3. Bezdek, J.C.: Pattern Recognition With Fuzzy Objective Function Algorithms. Plenum, New York (1981)

    Book  Google Scholar 

  4. Blake, C.L., Merz, C.J.: UCI repository of machine learning databases, a huge collection of artificial and real-world data sets (1998). https://archive.ics.uci.edu/ml/datasets.html

  5. Chang, S.T., Lu, K.P., Yang, M.S.: Fuzzy change-point algorithms for regression models. IEEE Trans. Fuzzy Syst. 23, 2343–2357 (2015)

    Article  Google Scholar 

  6. Chen, S.C., Zhang, D.Q.: Robust image segmentation using FCM with spatial constrains based on new kernel-induced distance measure. IEEE Trans. Syst. Man Cybern. -B 34, 1907–1916 (2004)

    Google Scholar 

  7. Dembélé, D., Kastner, P.: Fuzzy c-means method for clustering microarray data. Bioinformatics 19, 973–980 (2003)

    Article  Google Scholar 

  8. Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters. J. Cybern. 3, 32–57 (1974)

    Article  MathSciNet  Google Scholar 

  9. Izakian, H., Pedrycz, W., Jamal, I.: Clustering spatiotemporal data: An augmented fuzzy c-means. IEEE Trans. Fuzzy Syst. 21, 855–868 (2013)

    Article  Google Scholar 

  10. Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern Recogn. Lett. 31, 651–666 (2010)

    Article  Google Scholar 

  11. Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)

    Book  Google Scholar 

  12. Lubischew, A.A.: On the use of discriminant functions in taxonomy. Biometrics 18, 455–477 (1962)

    Article  Google Scholar 

  13. MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium, vol. 1, pp. 281–297 (1967)

    Google Scholar 

  14. Pollard, D.: Quantization and the method of k-means. IEEE Trans. Inf. Theory 28, 199–205 (1982)

    Article  MathSciNet  Google Scholar 

  15. Ruspini, E.: A new approach to clustering. Inf. Control 15, 22–32 (1969)

    Article  Google Scholar 

  16. Wu, K.L., Yang, M.S.: Alternative c-means clustering algorithms. Pattern Recogn. 35, 2267–2278 (2002)

    Article  Google Scholar 

  17. Yager, R.R., Filev, D.P.: Approximate clustering via the mountain method. IEEE Trans. Syst. Man Cybern. 24, 1279–1284 (1994)

    Article  Google Scholar 

  18. Yang, M.S.: A survey of fuzzy clustering. Math. Comput. Model. 18, 1–16 (1993)

    Article  MathSciNet  Google Scholar 

  19. Yang, M.S., Nataliani, Y.: Robust-learning fuzzy c-means clustering algorithm with unknown number of clusters. Pattern Recogn. 71, 45–59 (2017)

    Article  Google Scholar 

  20. Yang, M.S., Tian, Y.C.: Bias-correction fuzzy clustering algorithms. Inf. Sci. 309, 138–162 (2015)

    Article  Google Scholar 

  21. Yang, M.S., Wu, K.L.: A similarity-based robust clustering method. IEEE Trans. Pattern Anal. Mach. Intell. 26, 434–448 (2004)

    Google Scholar 

  22. Yang, M.S., Wu, K.L.: A modified mountain clustering algorithm. Pattern Anal. Appl. 8, 125–138 (2005)

    Article  MathSciNet  Google Scholar 

  23. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

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Correspondence to Miin-Shen Yang .

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Yang, MS., Chang-Chien, SJ., Nataliani, Y. (2018). Gaussian-kernel c-means Clustering Algorithms. In: Fagan, D., Martín-Vide, C., O'Neill, M., Vega-Rodríguez, M.A. (eds) Theory and Practice of Natural Computing. TPNC 2018. Lecture Notes in Computer Science(), vol 11324. Springer, Cham. https://doi.org/10.1007/978-3-030-04070-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-04070-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04069-7

  • Online ISBN: 978-3-030-04070-3

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